Contents

The amount of electric current (measured in amperes) through some surface, e.g., a section through a copper conductor, is defined as the amount of electric charge (measured in coulombs) flowing through that surface over time. If Q is the amount of charge that passed through the surface in the time T, then the average current I is:

By making the measurement time T shrink to zero, we get the instantaneous current i(t) as:

In solidconductive metal, a large population of electrons are mobile or "free" electrons. These electrons are bound to the metal lattice but not to any individual atom. Even without an external electric field applied, these electrons move about randomly due to thermal energy but on average, there is zero net current within the metal. Given an imaginary plane through which the wire passes, the number of electrons moving from one side to the other in any period of time is exactly equal to the number passing in the opposite direction.

A typical metal wire for electrical conduction is the stranded copperwire.

When a metal wire is connected across the two terminals of a DCvoltage source such as a battery, the source places an electric field across the conductor. The moment contact is made, the free electrons of the conductor are forced to drift toward the positive terminal under the influence of this field. The free electron is therefore the current carrier in a typical solid conductor. For an electric current of 1 ampere rate, 1 coulomb of electric charge (which consists of about 6.242 × 1018 electrons) drifts every second through the imaginary plane through which the conductor passes.

The current I in amperes can be calculated with the following equation:

Current density is a measure of the density of electrical current. It is defined as a vector whose magnitude is the electric current per cross-sectional area. In SI units, the current density is measured in amperes per square meter.

The mobile charged particles within a conductor move constantly in random directions. In order for a net flow of charge to exist, the particles must also move together with an average drift rate. Electrons are the charge carriers in metals and they follow an erratic path, bouncing from atom to atom, but generally drifting in the direction of the electric field. The speed at which they drift can be calculated from the equation:

where

is the electric current

is number of charged particles per unit volume

is the cross-sectional area of the conductor

is the drift velocity, and

is the charge on each particle.

Electric currents in solid matter are typically very slow flows. For example, in a copperwire of cross-section 0.5 mm², carrying a current of 5 A, the drift velocity of the electrons is of the order of a millimetre per second. To take a different example, in the near-vacuum inside a cathode ray tube, the electrons travel in near-straight lines ("ballistically") at about a tenth of the speed of light.

However, we know that electrical signals are electromagnetic waves which propagate at very high speed outside the surface of the conductor (moving at the speed of light, as can be deduced from Maxwell's Equations). For example, in AC power lines, the waves of electromagnetic energy propagate rapidly through the space between the wires, moving from a source to a distant load, even though the electrons in the wires only move back and forth over a tiny distance. Although the velocity of the flowing charges is quite low, the associated electromagnetic energy travels at the speed of light. The ratio of the signal velocity through a medium versus the speed of light in a vacuum is called the velocity factor.

The nature of these three velocities can be clarified by analogy with the three similar velocities associated with gases. The low drift velocity of charge carriers is analogous to air motions; to wind. The large signal velocity is roughly analogous to the rapid propagation of sound waves, while the large random motion of charges is analogous to heat; to the high thermal velocity of randomly vibrating gas particles.

Scheme of a discharging galvanic cell: The electric current is carried by electrons outside the cell (electric current going the opposite way of the electrons), and is carried by positively charged cations inside the cell (electric current going in the same way as the anions)

Conventional current was defined early in the history of electrical science as a flow of positive charge. In solid metals, like wires, the positive charges are immobile, and only the negatively charged electrons flow in the direction opposite conventional current, but this is not the case in most non-metallic conductors. In other materials, charged particles flow in both directions at the same time. Electric currents in electrolytes are flows of electrically charged atoms (ions), which exist in both positive and negative varieties. For example, an electrochemical cell may be constructed with salt water (a solution of sodium chloride) on one side of a membrane and pure water on the other. The membrane lets the positive sodium ions pass, but not the negative chloride ions, so a net current results. Electric currents in plasma are flows of electrons as well as positive and negative ions. In ice and in certain solid electrolytes, flowing protons constitute the electric current. To simplify this situation, the original definition of conventional current still stands.

There are also instances where the electrons are the charge that is moving, but where it makes more sense to think of the current as the movement of positive "holes" (the spots that should have an electron to make the conductor neutral). This is the case in a p-type semiconductor.

When studying electrical circuits, it is possible that the actual direction of current flow in a specific circuit element is not known at the start. Consequently, we arbitrarily assign each current variable a reference direction. After current values are solved for, some of them might display negative values. Hence, for the negative current variables, the actual current flows in the direction opposite to the reference direction which was originally selected.

The most obvious hazard is electrical shock, where a current passing through part of the body can cause a slight tingle, to cardiac arrest, or severe burns. It is the amount of current passing through the body that determines the effect, and this depends on the nature of the contact, the condition of the body part, the current path through the body and the voltage of the source. The effect also varies considerably from individual to individual. (For approximate figures see Shock Effects under electric shock.)

Electric arcs, which can occur with supplies of any voltage (for example, a typical arc welding machine has a voltage between the electrodes of just a few tens of volts), are very hot and emit ultra-violet (UV) and infra-red radiation (IR). Proximity to an electric arc can therefore cause severe thermal burns, and UV is damaging to unprotected eyes and skin.

Accidental electric heating can also be dangerous. An overloaded power cable is a frequent cause of fire. A battery as small as an AA cell placed in a pocket with metal coins can lead to a short circuit heating the battery and the coins which may inflict burns. NiCad, NiMh cells, and Lithium batteries are particularly risky because they can deliver a very high current due to their low internal resistance.